Relations among the light-cone quark models with the invariant meson mass scheme and the model prediction of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>−</mo><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math></span> mixing angle

Ho-Meoyng Choi; Chueng-Ryong Ji

doi:10.1103/PhysRevD.56.6010

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Relations among the light-cone quark models with the invariant meson mass scheme and the model prediction of the $η - η^{'}$ mixing angle

Ho-Meoyng Choi and Chueng-Ryong Ji

Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202

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Phys. Rev. D 56, 6010 – Published 1 November, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.6010

Abstract

We analyze the relations among the light-cone quark models which are based on the invariant meson mass scheme. We find that the difference from the Jacobi factor in model wave functions is substantially reduced in the numerical predictions for the physical observables once the best fit parameters are chosen. The difference in the choice of radial wave function [e.g., harmonic oscillator (HO) wave function versus power-law wave function] is, however, still appreciable even though the best fit parameters are used. We also observe an excellent agreement between the HO model predictions and the experimental data on the radiative decays of pseudoscalar $(P)$ and vector $(V)$ mesons and $P \to γ γ$ processes, if we use the constraint obtained by the axial anomaly plus partial conservation of axial-vector current relations and choose the $η - η^{'}$ mixing angle $θ_{SU (3)}$ $\approx - 19 ° .$

References (14)

T. Huang, B.-Q. Ma, and Q.-X. Shen, Phys. Rev. D 49, 1490 (1994).
F. Coester, in Constraint’s Theory and Relativistic Dynamics, edited by G. Longhi and L. Lusanna (World Scientific, Singapore, 1987), p. 159; in The Three-Body Force in the Three-Nucleon System, edited by B. L. Berman and B. F. Gibson (Springer, New York, 1986), p. 472.
V. A. Karmanov, Nucl. Phys. B166, 378 (1980); B362, 331 (1981).
P. L. Chung, F. Coester, and W. N. Polyzou, Phys. Lett. B 205, 545 (1988).
F. Cardarelli et al., Phys. Lett. B 332, 1 (1994); , Phys. Rev. D 53, 6682 (1996).
W. Jaus, Phys. Rev. D 44, 2851 (1991).
F. Schlumpf, Phys. Rev. D 50, 6895 (1994). In his work, the model parameters $m_{s}$ and $β_{s \bar{s}}$ of the vector mesons were not considered. However, we include these parameters in our analysis to compare with other models such as $H,$ $C,$ and $J .$
G. P. Lepage, S. J. Brodsky, T. Huang, and P. B. Mackenzie, in Particles and Fields-2, Proceedings of the Banff Summer Institute, Banff, Alberta, 1981, edited by A. Z. Capri and A. N. Kamal (Plenum, New York, 1983), p. 83.
Particle Data Group, R. M. Barnett et al., Phys. Rev. D 54, 1 (1996).
S. R. Amendolia et al., Phys. Lett. 146B, 116 (1984).
S. L. Adler, Phys. Rev. 117, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969).
J. Gasser and H. Leutwyler, Nucl. Phys. B250, 465 (1985).
C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1985), p. 550.
J. F. Donoghue, B. R. Holstein, and Y. C. R. Lin, Phys. Rev. Lett. 55, 2766 (1985).

[c1] T. Huang, B.-Q. Ma, and Q.-X. Shen, Phys. Rev. D 49, 1490 (1994).

[c2] F. Coester, in Constraint’s Theory and Relativistic Dynamics, edited by G. Longhi and L. Lusanna (World Scientific, Singapore, 1987), p. 159; in The Three-Body Force in the Three-Nucleon System, edited by B. L. Berman and B. F. Gibson (Springer, New York, 1986), p. 472.

[c3] V. A. Karmanov, Nucl. Phys. B166, 378 (1980); B362, 331 (1981).

[c4] P. L. Chung, F. Coester, and W. N. Polyzou, Phys. Lett. B 205, 545 (1988).

[c5] F. Cardarelli et al., Phys. Lett. B 332, 1 (1994); , Phys. Rev. D 53, 6682 (1996).

[c6] W. Jaus, Phys. Rev. D 44, 2851 (1991).

[c7] F. Schlumpf, Phys. Rev. D 50, 6895 (1994). In his work, the model parameters $m_{s}$ and $β_{s \bar{s}}$ of the vector mesons were not considered. However, we include these parameters in our analysis to compare with other models such as $H,$ $C,$ and $J .$

[c8] G. P. Lepage, S. J. Brodsky, T. Huang, and P. B. Mackenzie, in Particles and Fields-2, Proceedings of the Banff Summer Institute, Banff, Alberta, 1981, edited by A. Z. Capri and A. N. Kamal (Plenum, New York, 1983), p. 83.

[c9] Particle Data Group, R. M. Barnett et al., Phys. Rev. D 54, 1 (1996).

[c10] S. R. Amendolia et al., Phys. Lett. 146B, 116 (1984).

[c11] S. L. Adler, Phys. Rev. 117, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969).

[c12] J. Gasser and H. Leutwyler, Nucl. Phys. B250, 465 (1985).

[c13] C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1985), p. 550.

[c14] J. F. Donoghue, B. R. Holstein, and Y. C. R. Lin, Phys. Rev. Lett. 55, 2766 (1985).

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Relations among the light-cone quark models with the invariant meson mass scheme and the model prediction of the $η - η^{'}$ mixing angle

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Relations among the light-cone quark models with the invariant meson mass scheme and the model prediction of the η−η′ mixing angle

Abstract

References (14)

Relations among the light-cone quark models with the invariant meson mass scheme and the model prediction of the $η - η^{'}$ mixing angle